Dynamic mobility of rodlike goethite particles.

In this work we consider how the spheroidal shape of colloidal particles and their concentration in suspension influence their electrokinetic properties in alternating (ac) electric fields, in particular, their electrophoretic mobility, traditionally known as dynamic mobility in the case of ac fields. Elaboration of a formula for the mobility is based on two previous models related to the electrokinetic response of spheroids in dilute suspensions, completed by means of an approximate formula to account for the finite concentration of particles. At the end, semianalytical formulas have been obtained in the form of the classical Helmholtz-Smoluchowski equation for the mobility with three frequency-dependent factors, each dealing with inertia relaxation, electric double layer polarization and volume fraction effects. The two resulting expressions differ basically in their consideration of double layer polarization processes, as one considers only Maxwell-Wagner-O'Konski polarization (related to the mismatch between the conductivities of the particles plus their double layers and the liquid medium), and the other also includes the concentration polarization effect. Since in the frequency range typically used in dynamic mobility measurements the latter polarization has already relaxed, both models are capable of accounting for the dynamic mobility data experimentally obtained on elongated goethite particles in the 1-18 MHz frequency range. Results are presented concerning the effects of volume fraction, ionic strength, and pH, and they indicate that the models are good descriptions of the electrokinetics of these systems, and that dynamic mobility is very sensitive not only to the zeta potential of the particles, but also to their concentration, shape, and average size, and to the stability of the suspensions. The effects of ionic strength and pH on the dynamic mobility are very well captured by both models, and a consistent description of the dimensions and zeta potentials of the particles is reached. Increasing the volume fraction of the suspensions produces mobility variations that are only partially described by the theoretical calculations due to the likely flocculation of the particles, mainly associated with the fact that goethite particles are not homogeneously charged, with attraction between positive and negative patches being possible.